A pork roast was taken out of a hardwood smoker when its internal temperature had reached 180 degrees Fahrenheit and it was allowed to rest in a 75 degrees Fahrenheit house for 20 minutes after which its internal temperature had dropped to 170 degrees Fahrenheit. We will assume the temperature of the roast follows Newton's Law of Cooling, T(t) = Ta +(To - Ta)e-kt, where To is the inital temperature, Ta is the ambient temperature, and k is a decay constant. ("Ambient temperature" means the temperature of the space the object is in.) (a) Find the values of To and Ta for this problem. (b) Find the value of k for this problem. Then write down the function T(t) which gives the temper- ature of the pork roast in degrees Fahrenheit as a function of time t in minutes. (c) Find the time at which the roast dropped to 160 degrees Fahrenheit.
A pork roast was taken out of a hardwood smoker when its internal temperature had reached 180 degrees Fahrenheit and it was allowed to rest in a 75 degrees Fahrenheit house for 20 minutes after which its internal temperature had dropped to 170 degrees Fahrenheit. We will assume the temperature of the roast follows Newton's Law of Cooling, T(t) = Ta +(To - Ta)e-kt, where To is the inital temperature, Ta is the ambient temperature, and k is a decay constant. ("Ambient temperature" means the temperature of the space the object is in.) (a) Find the values of To and Ta for this problem. (b) Find the value of k for this problem. Then write down the function T(t) which gives the temper- ature of the pork roast in degrees Fahrenheit as a function of time t in minutes. (c) Find the time at which the roast dropped to 160 degrees Fahrenheit.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Set 2: A pork roast was taken out of a hardwood smoker when its internal temperature had reached 180
degrees Fahrenheit and it was allowed to rest in a 75 degrees Fahrenheit house for 20 minutes after
which its internal temperature had dropped to 170 degrees Fahrenheit. We will assume the temperature
of the roast follows Newton's Law of Cooling,
T(t) = Ta +(To-Ta)e-kt,
where To is the inital temperature, Ta is the ambient temperature, and k is a decay constant. ("Ambient
temperature" means the temperature of the space the object is in.)
(a) Find the values of To and Ta for this problem.
(b) Find the value of k for this problem. Then write down the function T(t) which gives the temper-
ature of the pork roast in degrees Fahrenheit as a function of time t in minutes.
(c) Find the time at which the roast dropped to 160 degrees Fahrenheit.
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